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Popular >

integral of 1+2/y

Solution

\int 1 + \frac{2}{y} d y

Solution

y + 2 ln ∣ y ∣ + C

Solution steps

\int 1 + \frac{2}{y} d y

Apply the Sum Rule:

\int f (x) \pm g (x) d x = \int f (x) d x \pm \int g (x) d x

= \int 1 d y + \int \frac{2}{y} d y

\int 1 d y = y

\int \frac{2}{y} d y = 2 ln ∣ y ∣

= y + 2 ln ∣ y ∣

Add a constant to the solution

= y + 2 ln ∣ y ∣ + C

Popular Examples

derivative of 1/(2z^3)derivative of

\frac{1}{2 z ^{3}}

y^'=-(2y)/(x+1)+2x

y^{^{'}} = - \frac{2 y}{x + 1} + 2 x

limit as x approaches 4 of x^2-1

x \to 4 lim (x^{2} - 1)

integral of xln^5(x)

\int x ln^{5} (x) d x

derivative of f(x)=x^4sin(4x)derivative of

f (x) = x^{4} sin (4 x)

Frequently Asked Questions (FAQ)

What is the integral of 1+2/y ?
The integral of 1+2/y is y+2ln|y|+C